Optical Based Pose Detection For Multiple Unmanned Underwater Vehicles

ABSTRACT

A system and method for optical communication between multiple UUVs, more specifically, for leader-follower formations between UUVs. The system focuses on the characterization and modeling of a 1-dimensional and/or 3-dimensional light field produced from a light source mounted on a Leader UUV, which is detected by one or more follower UUVs. Communication algorithms are used to monitor the UUV&#39;s motion and orientation utilizing simulators, look up tables, and the like. A variety of detectors arrays can be used in a variety of wavelengths depending on the desired application.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application claims the benefit of Provisional PatentApplication Ser. No. 61/976,802 filed Apr. 8, 2014, which isincorporated herein by reference.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

This invention was made with government support. The government hascertain rights in the invention.

FIELD OF THE INVENTION

The present invention relates to unmanned underwater vehicles (UUVs) andmore particularly to a method and system to use pose detection inmultiple degrees of freedom to produce coordinated motion betweenmultiple UUVs.

BACKGROUND OF THE INVENTION

Unmanned Underwater Vehicles (UUVs) are used in underwater operationsthat are difficult and dangerous for human divers. Such operationsinclude search and rescue missions, inspection of large underwaterstructures, bathymetry exploration, underwater pipeline and cableinstallations, military applications such as minesweeping, harbormonitoring and submarine detection, investigations of shipwrecks,non-invasive observation of marine wildlife and sea/ocean floors, andthe like. Developing a Dynamic Positioning (DP) system using opticalcommunication sensor systems would enable the simultaneous control ofmultiple UUVs. With the use of a multiple UUV system, instead of usingonly a single UUV at a time, the efficiency of performing underwateroperations would be significantly increased, reducing mission time andcosts. In addition, by using cost-efficient optical sensors, as opposedto expensive acoustic sensors, operating and manufacturing these UUVsystems would further reduce UUV mission costs. Because of thisresearch, UUV systems could be more widely accessible and could moreeffectively help perform dangerous underwater operations without risk tohuman divers.

SUMMARY OF THE INVENTION

It has been recognized that developing a Dynamic Positioning (DP) systemusing optical communication sensor systems would enable the simultaneouscontrol of multiple UUVs. Typically, the applications that utilize UUVstake place in deep-sea environments and include heavy-duty tasks thatmay take a long time and therefore, are not suitable to be performed bydivers. In certain embodiments of the present invention, multiple UUVscan be used simultaneously for these tasks and can be controlled by oneoperator using a leader-follower system. In typical UUV leader-followerformation systems acoustics are used as the main method of communicationbetween the vehicles. However, hardware (e.g., acoustic transducers) canbe very costly and are limited by the logistics required in modifyingthe leader UUV. Optical communication modules can provide an alternativecost-efficient approach. In certain embodiments of the presentinvention, an optical communication link between UUVs is used to form aleader follower formation. UUV's use light sources to illuminate theseafloor, and in certain embodiments, this hardware can be used as abeacon for aligning follower UUVs.

These aspects of the invention are not meant to be exclusive and otherfeatures, aspects, and advantages of the present invention will bereadily apparent to those of ordinary skill in the art when read inconjunction with the following, description, appended claims, andaccompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

The foregoing and other objects, features, and advantages of theinvention will be apparent from the following description of particularembodiments of the invention, as illustrated in the accompanyingdrawings in which like reference characters refer to the same partsthroughout the different views. The drawings are not necessarily toscale, emphasis instead being, placed upon illustrating the principlesof the invention.

FIG. 1A is a schematic illustration of a circular array used in oneembodiment of the present invention.

FIG. 1B(1) is a schematic illustration of a planar array used in oneembodiment of the present invention.

FIG. 1B(2) is a schematic illustration of a planar array used in oneembodiment of the present invention.

FIG. 1C graphically represents the inverse square law as it relates toocean optics.

FIG. 1D graphically represents the Beer-Lambert law as it relates toocean optics.

FIG. 2A is a schematic of an experimental set up for one embodiment thepresent invention.

FIG. 2B represents the modeling and control of one embodiment of thesystem of unmanned underwater vehicles of the present invention.

FIG. 3 shows light attenuation results for one embodiment of the presentinvention.

FIG. 4A is a plot of the cross section beam pattern of one embodiment ofthe present invention.

FIG. 4B shows plots for normalized intensity versus distance for certainembodiments of the present invention.

FIG. 5 shows one embodiment of the system of the present invention.

FIG. 6 shows one embodiment of the system of the present invention.

FIG. 7 shows a reference image compared to a detected image for oneembodiment of the system of the present invention.

FIG. 8 represents one embodiment of a look op table of the system of thepresent invention.

FIG. 9 shows the leader follower behavior for one embodiment of thesystem of the present invention.

FIG. 10 shows a plot of leader follower behavior for one embodiment ofthe system of the present invention.

FIG. 11 shows a plot of leader follower behavior for one embodiment ofthe system of the present invention.

FIG. 12 shows a plot of leader follower behavior for one embodiment thesystem of the present invention.

FIG. 13 shows key image parameters and intensity profiles for a planararray detector unit of one embodiment of the present invention withhardware and environmental background noise.

FIG. 14 shows key image parameters and intensity profiles for a curvedarray detector unit of one embodiment of the present invention withhardware and environmental background noise.

FIG. 15 shows comparative resemblance results of one embodiment of thepresent invention (SAM angles) for 21×21 element curved and planar array(at x=4 m) as a function of: (a) lateral translation, (b) yaw rotation.

FIG. 16 shows comparative resemblance results of one embodiment of thepresent invention (i.e., SAM angle) with respect to varying array sizes(incorporating environmental and background noise): (a) SAM angle withrespect to lateral motion (b) SAM angle with respect to angularrotation.

FIG. 17 shows comparative resemblance results of one embodiment of thepresent invention (i.e., SAM angle) with respect to operational distance(incorporating environmental and background noise): (a-c) lateral shift,(d-f yaw rotation—(a, d) 3×3 array (b, e) 5×5 array (c, f) 101×101array.

FIG. 18 shows arrays for embodiments of the present invention.

FIG. 19 shows detected images for embodiments of the present invention.

FIG. 20 shows detected images for embodiments of the present invention.

FIG. 21 shows detected images for embodiments of the present invention.

FIG. 22 shows detected images for embodiments of the present invention.

DETAILED DESCRIPTION OF THE INVENTION

Over the past few decades, the control and mechanics of UUVs haveadvanced to allow commercial underwater operations, such as inspectionof underwater infrastructure, seafloor mapping, the installation ofcables and pipes, and the like. The use of multiple UUVs, as opposed toa single UUV, for any such mission can reduce survey/operation time andimprove overall system performance. However, enabling communicationbetween all UUVs in order to control the position of the entire UUVfleet (i.e., formation control) is a challenge. One approach is tocontrol a single UUV (the Leader) that the rest of the UUVs (theFollowers) would align in a pre-determined formation. The key to thisapproach is a cost-efficient sensor communication system between theLeader and each of the Followers. This communication system would allowfor a larger variety of UUV formations for a variety of underwatertasks.

Most studies on inter-communication between UUVs have concentrated onacoustic communication, which has noted performance over long distances.However, the required hardware is costly and requires significantpayload considerations in UUV platform design. A cost-effectivealternative is optical communication, which can use either existinghardware (e.g., light sources as beacons) or additional hardware (e.g.,commercial off the shelf (COTS) components) at low cost.

Modern spacecraft and aircraft currently use optical communication fornavigation, docking and data transfer. The challenge of underwateroptical communication, however, is that water scatters and absorbs lightsignificantly greater than it would in air. As a result, thecommunication ranges under water tend to be much shorter, in addition,water as a medium is not homogeneous and is constantly changing. Thus,it is difficult to predict the varying optical properties of the water(e.g., diffuse attenuation coefficient and scattering) during UUVoperation.

One aspect of the present invention is an optical communicationinstrumentation system for leader-follower formations between UUVs. Incertain embodiments, the UUVs are Remotely Operated Vehicles (ROVs). Incertain embodiments, the system focuses on the characterization andmodeling of a 1-dimensional and/or 3-dimensional light field producedfrom a light source mounted on a Leader UUV. Based on the light fieldmeasurements, a prototype optical detector array for the follower UUVwas developed. In addition, communication algorithms to monitor theUUV's motion were developed and evaluated. These tests were conductedusing both numerically simulated software and through physicalunderwater experiments.

Applicants' own work included the development of a design forcontrolling distance detection of UUVs using optical sensor feedback ina Leader-Follower formation. The distance detection algorithms detectedtranslational motion above water utilizing a beam of light for guidance.The light field of the beam was modeled using a Gaussian function as afirst-order approximation. This light field model was integrated intonon-linear UUV equations of motion for simulation to regulate thedistance between the leader and the follower vehicles to a specifiedreference value. A prototype design of a photodetector array consistingof photodiodes was constructed and tested above water. However, beforean array was mounted on the bow of the follower UUV, a betterunderstanding of the underwater light was needed. The proposed systemwas based on detecting the relative light intensity changes on thephotodiodes in the array.

There are several possible geometric shapes for use as optical detectorarrays. The two most common array designs in literature are planar andcurved. Each design has its own benefits. A curved array (FIG. 1A)requires less optical elements and aberrations are reduced. Aplanar-array (FIG. 1B(1)) can maximize the clarity of its signal(against existing measurement noise) between all its elements.Currently, the extent of research of optical communication for UUVs isvery limited and has focused mainly on planar arrays as detector unitsfor Autonomous Underwater Vehicles (AUVs). These studies include anestimation of AUV orientation with respect to a beacon by using aphotodiode array and distance measurement between two UUVs. In additionto array design for communication between UUVs, other studies haveinvestigated optical communications for docking operations, where AUVsare able to transmit their collected data and recharge their batteriesby docking with an underwater station. This capability eliminates theneed for human interruption during these tasks and significantly reducesmission time and costs.

One example used for docking operations was the use of a single detector(quadrant photodiode) in a 2×2 detector array, which was mounted on anAUV and used to detect translational motion of the AUV with respect toan external light source. The optical communication methods mentionedabove were able to measure only one to three degrees of freedom (DOF)and only in pure translation and not rotation. However, UUVs maneuver insix DOF (three in translation and three in rotation). Therefore, thedesign of an optical detector array of the present invention is crucialfor motion detection in all six DOF.

In certain embodiments of the present invention the characterization ofthe optical components define: 1) the geometrical shape of the opticaldetector array, 2) the minimum number of optical elements required touniquely determine pose (position and orientation) feedback, and 3) thespectral characteristics (e.g., the wavelength band of the light source,the optical detectors, and the like).

In certain embodiments of the present inventions, the curved array wasable to detect motion much more effectively than the planar array. Thecurved, array was more sensitive to the light field input, resulting inimproved translational and rotational motion distinctions over that ofthe planar array. Furthermore, changes in positional and rotationalshifts can be detected by an array consisting of a minimum of 5×5optical elements.

In one embodiment of the present invention, a curved 5×5 optical arraywas used for optical communication system for UUVs. In addition to thephysical characteristics of the detector, the spectral characteristicsof the light source-optical detector pair is also crucial and should beidentified properly. In certain embodiments, the system showed thatmaximum light penetration occurred between the wavelength band of500-550 nm. In certain embodiments, a green light source (bandwidthbetween 500-500 nm) and a detector with peak responsivity within 500-550nm was used. Preliminary evaluation of the communication algorithmsbased on simulator outputs showed good performance in the detection oftranslational and rotational motion of a leader UUV.

In certain embodiments, measurements and calibration of a light fieldvia an optical detector array mounted on a follower ROV wasaccomplished. Follower ROV dynamic positioning algorithms based upon theacquired light field calibration are also used in certain embodiments ofthe present invention. In certain embodiments, look-up tables arederived from positional and rotational offset measurements between thelight source and the detector array. These look-up tables are then usedto develop dynamic positioning (DP) algorithms for a multiple ROV systemusing advanced control techniques. DP algorithms are developed usingnumerical simulation software. In certain embodiments, multiple ROVs areequipped with the developed optical communication system and tested tovalidate the performance of the optical based DP.

The dynamic positioning of UUVs of the present invention use opticalfeedback to maneuver multiple UUVs in precisely controlled formation.The optical instrumentation system of the present invention is alsoapplicable to static operations such as UUV docking. The system of thepresent invention will significantly decrease underwater mission timeand costs without risking the safety of human divers.

UUVs can be classified into two groups; 1) remotely operated vehicles(ROVs) and 2) autonomous underwater vehicles (AUVs). ROVs differ fromAUVs because they are remotely operated and they require an umbilicalcable from a surface vessel in order to provide power and to send andreceive communication signals (e.g., video and control signals) betweenthe ROV pilot and the ROV itself. On the contrary, AUVs are powered byonboard batteries and do not need human interaction while operating.AUVs have pre-defined trajectories for their tasks. As a result, AUVsare more affordable to operate than ROVs.

Some applications that employ AUVs involve collecting data in underwaterenvironments using onboard sensors. These applications can be performedin a quicker and more efficient fashion if more than one AUV is used. Tomake this happen, it is imperative that the AUVs communicate with eachother. In addition, these vehicles may be required to maintain aspecific formation such as leader-follower configuration in which one ofthe vehicles is assigned as a leader and the other vehicles track itspath.

In certain embodiments of the present invention, a ROV is followed withone or more AUVs in leader-follower formation by utilizing opticalsensors for inter-vehicle communications. Research in leader-followerformation to date has focused almost exclusively on using acoustics forcommunications, but studies have shown that underwater communicationwith acoustics has its constraints like transmission delays, multi-pathfading, directional and bandwidth limitations due to the harsh oceanenvironment, and the like. In addition to tracking a leader robot usingoptical sensors, the system of the present invention will utilizeseveral trajectory control algorithms on the follower robot (AUV). Incertain embodiments of the present invention, an AUV is followed withone or more AUVs in leader-follower formation by utilizing opticalsensors for inter-vehicle communications.

In certain embodiments, a ROV may be converted to an AUV by adding anonboard power supply and adjusting for the power distribution to theonboard computers and sensors. The sensors for communication between theleader and follower vehicles are then mounted and tested. In Applicants'initial studies, a ROV was commanded via a remote controller by anoperator on the surface. The ROV was elected as a leader while the AUVwas the follower for testing. The ROV, which was powered from thesurface via umbilical cable had a light emitter at its crest while theAUV possessed an electro-optical optical sensor located at its bow todetect the light. The photodiode on the AUV had 4 equally dicedquadrants and was able to tell in which part the light was concentrated,thus the location of the leader was detected. After the AUV detected thelight, several trajectory control algorithms on the AUV were tested inorder to determine the optimal tracking algorithm.

It is known that light is attenuated underwater over long distances.However it has been shown that data acquisition using optical sensorscan be accomplished at 10-15 meters for very turbid water and 20-28meters in clearer water. Previous studies have shown guidance ofunmanned underwater vehicles that is roughly analogous to that which isemployed by a heat-seeking air-to-air missile when locked onto a target.In that case the target was a light emitter which was located at anunderwater dock. When the light propagated in the absorbing, scatteringmedium such as seawater and it was subsequently imaged by a lens locatedat a distance the photons emitted by the source experienced four generaloutcomes: some were absorbed by the medium, others were scatteredoutside of the field-of-view of the detector, others were scattered intothe detector's field-of-view and a few photons remained unscattered. Thestudies found that light in the first two categories never reached thetracker and represented attenuation, which was overcome using a brighterbeacon. Scattered light within the field-of-view was imaged almostequally into each of four quadrants of a photo detector located near thefocal plane of an objective lens.

Underwater light is attenuated due to the optical characteristics of thewater, which are constantly changing and are not uniformly distributedAs a result, applying distance detection algorithms underwater addscomplexity and reduces operational ranges. In certain embodiment's, theoperation distance between the UUVs was limited to a range between 4.5to 8.5 m for best performance.

In certain embodiments, optical communication was based on the relativeintensity measured between the detectors within the photo-detector arraymounted on the follower ROV. The beam pattern produced by the lightsource was noted. The intensity of light underwater follows two basicoptics theories, the inverse square law and the Beer-Lambert law. See,for example, FIG. 1C and FIG. 1D.

In certain embodiments, the light field emitted from a light source canbe modeled with different mathematical functions. In addition, there area variety of light sources that can be used underwater that differ intheir spectral irradiance (e.g., halogen, tungsten, and metal-halide,and the like). The spectral characteristics of the light source affectthe illumination range, detector type and the detection algorithms. Justas the light sources do. The photodetectors also have a spectral widthin which their sensitivity is at a maximum value. In certainembodiments, determining the spectral characteristics of the lightsource, enable selection of the detector and filters for thephotodetector array.

It is assumed that the beam pattern can be modeled using a Gaussianfunction, particularly for a single point light source. The Gaussianmodel used in this study can be represented as follows:

I(θ)=A*exp(−B*θ ²)   (1)

In Equation 1, I is the intensity at a polar angle, θ, where the originof the coordinate system is centered around the beam direction of thelight source. A and B are constants that describe the Gaussian amplitudeand width respectively.

According to the inverse square law, the intensity of the light isinversely proportional to the inverse square of the distance:

I=S/4πr ²   (2)

where I is the intensity at r distance away from the source and S is thelight field intensity at the surface of the sphere. Thus, the ratio ofthe light intensities at two different locations at the same axis can beexpressed as:

I ₁ /I ₂=(S/4πr ₁ ²)/(S/4πr ₂ ²)=r ₁ ² /r ₂ ²   (3)

The light field S generated by a light source is assumed to show uniformillumination characteristics in all directions. In addition, the lightintensity is such that the light source is assumed to be a point sourceand that its intensity is not absorbed by the medium.

It should also be noted that although the inverse square law is thedominant concept in the development of control algorithms of the presentinvention, this is not the only dominant optical mechanism that affectsthe light passing in water. As the light travels through water, its raysget absorbed by the medium according to the Beer-Lambert law.Beer-Lambert law states that radiance at an optical path length, l, in amedium decreases exponentially depending on the optical length, l, theangle of incidence, θ, and the attenuation coefficient, K. Beer-Lambertlaw describes the light absorption in a medium under the assumption thatan absorbing, source-free medium is homogeneous and scattering is notsignificant. When the light travels through a medium, its energy isabsorbed exponentially

L(ζ, ξ)=L(0, ξ)exp(−ζ/μ)   (4)

where L denotes the radiance, ζ the optical depth, ξ the directionvector, and μ denotes the light distribution as a function of angle suchthat:

μ=cos θ  (5)

defining a quantity l, (i.e., the optical path length in direction μ),

dl=dζ/μ=K(z)dz/μ  (6)

where K(z) is the total beam attenuation coefficient and dz is thegeometric depth. The amount of attenuation depends on the distance zfrom the light source and the attenuation coefficient K. In thesepreliminary studies, the experimental setup was built such that theincidence angle θ was zero.

L(ζ, ξ)=L(0, ξ)exp(K(z)dz)   (7)

were L denotes the radiance and ξ is the directional vector. The diffuseattenuation factor in the Applicants' preliminary study was 0.0938 m⁻¹.Experimental, work was performed in order to evaluate proposed hardwaredesigns, which were based on ocean optics and the hardware restrictionsliar the prototype ROV system. The experiments included beamdiagnostics, spectral analysis and intensity measurements from severallight sources.

A light source was mounted on a rigid frame to the wall in a tow tankand a light detector was placed underwater connected to a tow carriage.See, for example. FIG. 2A. To characterize the interaction between thelight source and the light array a 50 W halogen lamp powered by 12 Vpower source was used. For the detector unit, a spectrometer (by OceanOptics Jaz) was used to characterize the underwater light field. Theseempirical, measurements were used to adjust the detection algorithms andwere also used in the design of a photo-detector array. The light sourcein the tank simulated a light source that was mounted on the crest of aleader ROV. The design of the photo-detector array simulated the arraythat would be mounted on the bow of a follower ROV. In certainembodiments, the photo-detector array design depends on the size of theROV and the light field produced by the light source mounted on theleader ROV. In this case, the size for an optical detector module waskept at 0.4 m, which is the width dimension of the prototype ROV.

Translational experiments in 1-D and 3-D (i.e., motion along andperpendicular to the center beam of the light source) were conducted inair and in water. The goals for the 1-D experiments were to characterizethe spectral properties of the water and to determine the best spectralranges for optical communication between the ROVs. In the underwaterexperiment, a submerged fiber optic cable with a collimator wasconnected to a spectrometer and was vertically aligned based on the peakvalue of radiance emitted from the light source. This alignment wasconsidered the illumination axis (z-axis). The radiance emitted from thelight source through the water column was empirically measured by thespectrometer at distances ranging from 4 m to 8 m at 1 m increments. Itis important to note that the distances were measured from the towcarriage to the wall of the tank and an additional 0.5 m offset distancewas added in the calculation to take into account the offset mounting ofthe light and spectrometer with respect to the wall of the tank and thetow carriage. The spectrometer was configured to average 40 samples withan integration time of 15 milliseconds. A 2° collimator was used torestrict the field of view collected by the spectrometer and to avoidthe collection of stray light rays reflecting off the tank walls or fromthe water surface.

The experimental setup in air was very similar, where the spectrometerwas mounted on a tripod and aligned to the peak value of radiance, theillumination axis (z-axis). Because such light sources produce heat athigh temperatures (up to 700° C.), the experimental setup in airrequired that the light source be submerged in an aquarium duringoperation. Similar to the underwater experiments, the same distancesbetween the light source and the spectrometer, including the offsets,were maintained.

The 3-D translational underwater experiments utilized the same setup asthat of the underwater 1-D experiments where additional radiancemeasurements were conducted along a normal axis (x-axis) located on aplane normal to the illumination axis (z-axis). The 3-D translationalexperiment maintained the same distances along the illumination axisbetween the light source and the spectrometer (i.e., 4 m to 8 m), whereadditional measurements were conducted along, the normal axis at 0.1 mincrements ranging from 0 m to 1 m. As mentioned previously, it isassumed that the light source produced a beam pattern that can bemodeled, using a Gaussian function. Accordingly, it was assumed that theradiance measurements along the normal axis were symmetric in alldirections. The diffuse attenuation coefficient, K, was used as aparameter to calculate the decreased amount of energy from the lightsource to the target. The diffuse attenuation coefficient was used todetermine the spectral range of the light source and determine thephoto-detector types that could be utilized in the array.

In certain embodiments, for successful optical communication up toranges of 9 m, the spectral ranges should be maintained such that thediffuse attenuation coefficient values are smaller than 0.1 m-1 m. Atthis distance, the signal loses about half its energy. As a first-orderapproximation, the diffuse attenuation coefficient values were assumedconstant throughout the water column. This assumption reduced the numberof parameters used in the distance detection algorithms and theprocessing time used in future controls applications. The diffuseattenuation coefficient values were calculated for a 50 W light source.

Diffuse attenuation was calculated. Measurements taken at a specificdistance in water and in air were compared in order to account for theinverse square law. The light that traveled in air also underwentdiffuse attenuation but it was ignored in this case. The valuessuggested that the wave tank, where the experiments were conducted,contained algae and dissolved matter. The study results suggested that500-550 nm band-pass filters in the range should be used in the detectorunit to provide better performance of the distance detection algorithms.

Referring to FIG. 3, it was seen that the spectral range between 500-550nm underwent the least attenuation at any given distance. Based on thelight attenuation results, the distance between the leader and thefollower vehicles was calculated. The experimental results showed thatthe performance of the algorithms in the water tank was expected todecrease after 8.5 m. Beyond this range, the light intensity fell intothe background noise level (i.e., <20%). The intensity readings werecollected between 500-550 nm and averaged. The experimental values werecompared with the theoretical. The measurement at 4.5 m was used as thereference measurement to normalize the intensity.

The light profile calculated from the 3-D experiments agreed with theassumption that the pattern of the light beam can be described using a2-D Gaussian fit. See, FIG. 4. Using a 50% intensity decrease as athreshold, the effective beam radios from the center (i.e., theillumination axis) was 0.3 m. Another key finding obtained from the 3-Dexperiments, was the dimensions of the light detector array. It wasshown that if the length of the array was kept at 0.6 m, then differentlight detector elements could detect the light intensity change, whichis useful information for control algorithms. It should he stated thatthe physical characteristics of the photo-detector array such asdimensions and the spacing between the array elements strictly depend onbeam divergence.

Referring to FIG. 4A, a plot of the cross-sectional beam pattern isshown. The measurements were collected from 0 to 1.0 m at x-axis and at4.5 m at the illumination axis for 50 W light source. The measurementsbetween 500-550 nm were averaged. FIG. 4B shows the normalized,intensity plotted against distance for certain embodiments of thepresent invention.

Referring to FIG. 5, one embodiment of the system of the presentinvention is shown. More particularly, a leader UUV and a follower UUVare shown. The leader UUV has a light source and the follower UUV has alight detector array. In certain embodiments, the UUVs are configured tomaintain relative x, y, z, and ψ coordinates between the two or moreUUVs using optical feedback.

Referring to FIG. 6, one embodiment of the system A the presentinvention is shown. More particularly, a leader UUV and a follower UUVare shown in the top of the figure. In certain embodiments, the leaderis a ROV. In certain embodiments, there are multiple follower UUVs. Incertain embodiments, the leader UUV has a light source and the one ormore follower UUV's has a light detector array. In certain, embodiments,the UUVs are configured to maintain relative x, y, z, and ψ coordinatesbetween the two or more UUVs using optical feedback.

According, to the calculated diffuse attenuation, a 500-550 nm band-passfilter allows for the observation at the light field from a singlesource as a 2-D Gaussian beam pattern. At this spectral range, around0.1 m-1 m, the peak power of the beam (along the z-axis) changed from100% to 23% as the array moved away from light from 4.5 m to a distanceof 8.5 m. The size of the beam pattern is a function of the divergenceangle of the beam. In certain embodiments, the FWHM radius expanded from0.3 m to 0.4 m as the array moved away from light from 4.5 m to adistance of 8.5 m. In certain embodiments, the beam divergence can bemodified using reflectors and optic elements in case more acute changesin the light field are needed over a shorter distance of 0.4 m.

While gathering empirical measurements in the test tank, several errorsources were identified that limited an accurate correlation between themodels and its corresponding measurements. These errors includedalignment errors and measurement errors underwater. Although the framemounting all the elements was rigid and aligned, the internal alignmentof the light source and of the detectors may not have been alignedperfectly along one axis. As a result, the profile measurements of lightalong the z-axis and the along the xy-plane might be slightly skewed.Another factor was the water turbidity. An accurate calculation of thewater turbidity is important. Therefore, for more accurate distancedetection algorithms, water turbidity should be taken into account aswell as proper alignment.

In certain embodiments of the system of the present invention, thesystem can be used in other applications, such as underwater opticalcommunication and docking. Underwater optical communication can providerates of up to 10 Mbits over ranges of 100 m. Several studies haveinvestigated the use of omnidirectional sources and receivers inseafloor observatories as a wireless optical communication. Anotherapplication is underwater docking by using optical sensors.

One aspect of the present invention is a system that controls therelative pose position between two or more UUVs using control algorithmsand optical feedback. In certain embodiments, the leader UUV isconfigured to have a light source at its crest, which acts as a guidingbeacon for the follower UUV that has a detector array at its bow. Posedetection algorithms are developed based on a classifier, such as theSpectral Angle Mapper (SAM), and chosen image parameters. In certainembodiments, an archive look-up table is constructed for varyingcombinations of 5-degree-of-freedom (DOF) motion (i.e., translationalong all three coordinate axes as well as pitch and yaw rotations). Incertain embodiments, leader and follower vehicles are simulated for acase in which the leader is directed to specific waypoints in ahorizontal plane and the follower is required to maintain a fixeddistance from the leader UUV. In certain embodiments of the presentinvention. Proportional-Derivative (PD) control, or the like, is appliedto maintain stability of the UUVs. Preliminary results indicate that thefollower UUV is able to maintain its fixed distance relative to theleader UUV to within a reasonable accuracy.

The UUVs kinematics are typically analyzed by using Newton's second lawas presented here,

τ=Mv+C(v)v+D(v)v+g(η)   (8)

The linear and angular velocity vector are represented in the bodycoordinate reference frame v ε

^(6×1). The UUVs mass and the hydrodynamic added mass derivatives arecomposed from the rigid body mass, M_(RB), and the added mass matrix,M_(A), (i.e. M_(A)=M_(RB)+M_(A)). The Coriolis and the centripetalforces are described as C(v)=C_(RB)(v)+C_(A)(v), where C_(RB)(v) andC_(A)(v) are derived from M_(RB) and M_(A) matrices, respectively. TheUUV is also subjected to gravitational forces and moments, g(η), as afunction position and attitude in the Earth-fixed reference frame, η ε

^(6×1). Lastly, the quadratic damping force on the UUV D(r) aredescribed by following matrix

${{D(v)}v} = \begin{bmatrix}{v^{T}\mspace{14mu} D_{1}\mspace{14mu} v} \\{v^{T}\mspace{14mu} D_{2}\mspace{14mu} v} \\{v^{T}\mspace{14mu} D_{3}\mspace{14mu} v} \\{v^{T}\mspace{14mu} D_{4}\mspace{14mu} v} \\{v^{T}\mspace{14mu} D_{5}\mspace{14mu} v} \\{v^{T}\mspace{14mu} D_{6}\mspace{20mu} v}\end{bmatrix}$

where D_(i) ε

^(6×6) is a function of water density, drag coefficient, and projectedcross-sectional area. The control input vector is derived with respectto the body coordinate frame, as the control input is applied to thebody. The body fixed reference frame is transformed into the Earth-fixedreference frame:

η₁ =J ₁(η₂)v ₂   (9)

where η=[x,y,z,φ,θ,ψ]^(T) is composed of translation along the x, y andz axes and roll, φ, pitch, θ, and yaw, ψ, rotations defined inEarth-fixed coordinates. Here, η ε

^(6×1) is the position and attitude state vector in the Earth-fixedcoordinate frame, i.e. η₁η₂T, were η₁ ε

^(3×1) corresponds to translational motion in the Earth-fixed referenceframe and η₂=[φ,θ,ψ]^(T) is the vector of Euler angles (using a 3-2-1rotation sequence) representing the vehicle attitude.

J₁η₂ is the transformation matrix from the body fixed coordinates toEarth-fixed coordinates) and is described as

${J_{1}\left( \eta_{2} \right)} = \begin{bmatrix}{c\; \psi \; c\; \theta} & {{{- s}\; \psi \; c\; \varphi} + {c\; \psi \; s\; \theta \; s\; \varphi}} & {{s\; \psi \; s\; \varphi} + {c\; \psi \; c\; \varphi \; s\; \theta}} \\{s\; \psi \; c\; \theta} & {{c\; \psi \; c\; \varphi} + {s\; \varphi \; s\; \theta \; s\; \psi}} & {{{- c}\; \psi \; s\; \varphi} + {s\; \theta \; s\; \psi \; c\; \varphi}} \\{{- s}\; \theta} & {c\; \theta \; s\; \varphi} & {c\; \theta \; s\; \varphi}\end{bmatrix}$

where s(.) and c(.) represents sine and cosine functions, respectively,while φ, θ and ψ are the corresponding roll, pitch and yaw anglesdefined in Earth-fixed coordinates, respectively. As such, thecorresponding attitude transformation matrix is an identity matrix suchthat J₁(η₂)=I_(3×3). Numerical integration results in the extraction ofUUV position in the Earth-fixed coordinate frame.

In certain embodiments, under the assumption that the leader UUV has aknown path a priori, the follower UUV can use information collected by aplanar or other detector array as feedback to determine the leader UUV'srelative pose η_(f)=η_(i)−η_(d) where η_(f) is the follower pose, η_(l)is the leader pose determined by the follower, and η_(d) is the desiredrelative pose, incorporating desired relative distance and attitude,between the leader and the follower UUVs. The control problem in thiscase can be evaluated as both a point-to point regulation problem andalso as a trajectory control problem. In certain embodiments, the leaderis given a reference input, i.e. step inputs, to travel to givenwaypoints while the follower generates its own time-varying trajectoryfrom the leader motion. The PD control of a nonlinear square system, hasbeen shown to be asymptotically stable using Lyapunov's Direct Method.

In certain embodiments of the present invention, the follower posedetection of the leader is based on the output image sampled by thefollower's detector consisting of an array of 21×21 detector elements.Specifically, the output image is the light field emitted from theleader's beacon that intersects with the planar detector array. Incertain embodiments, the control algorithms were tested using dataproduced from the detector array simulator developed by the Applicants.The input to the simulator is the relative pose geometry between theUUVs and the optical conditions of the medium. To extract the pose ofthe leader from the image, five main image parameters are used. Theseparameters are the Spectral Angle Mapper (SAM), the skewness of both therow and column of the resulting intensity profile, and the row andcolumn numbers of the image pixel with the highest intensity. SAM is ameasure of resemblance between a reference image and an image undertest. In certain embodiments, the reference image is the output obtainedfrom the detector array when the light source and the detector have anoffset along the x-axis only with no translation/rotation. In certainembodiments, the image under test is the output when there is a specificrelative pose between the leader and the follower. The SAM algorithm isgiven as

$a = {\cos^{- 1}\left( \frac{\overset{\rightarrow}{U_{t}} - \overset{\rightarrow}{V_{t}}}{\left. ||\overset{\rightarrow}{U_{t}}||{- \left. ||\overset{\rightarrow}{V_{t}} \right.||} \right.} \right)}$

where α is is the SAM angle which varies between 0° and 90° andincreases when the difference between the two images increases. U_(t)and V_(t) are the light intensity vectors obtained by the detectors forthe reference image and image under test, respectively.

The two other key image parameters are the skewness values of thehorizontal slope, Sk_(x), and the vertical slope, Sk_(y). The key inusing these parameters is that they do not require significantcomputational effort. This is a key advantage, as the performance of thecontrol system can degrade with increased computational delays.

Based on the location of the pixel with the maximum intensity, thehorizontal and vertical gradients of the image can be calculated. Theuse of the gradient of the intensities, rather than the intensityprofile itself, is advantageous as the slope provides bothdirectionality and asymmetry information. As an example, a referenceimage and sample detected image with the resulting horizontal andvertical profiles (showing the respective gradients in each direction)are provided in FIG. 7. Referring to FIG. 7, a reference image anddetected image are shown. Reference image (top left), Detected image(top right), y-axis intensity profile (bottom left), z-axis intensityprofile (bottom right).

In certain embodiments of the present invention, varying geometries weresimulated with a numerical simulator. For translation motion, e.g., yand z-axis motions, the detector array was moved from −0.3 m to 0.3 m at0.03 m increments. For rotational motion, e.g., pitch and yaw motion,the follower was rotated from −30° to 30° at 3° increments. The resultsfrom the simulations for each combination of motions were stored in aconsolidated data base, in the form of a look up table. The tableconsisted of the pose of the light source, i.e. x, y, z, ψ (yaw) and θ(pitch), the corresponding skewness values for the images, i.e., Sk_(x)and Sk_(y), α (SAM angle), and the row and column number of the pixelwith the highest intensity (See, for example, FIG. 8).

Referring to FIG. 8, the first four columns indicate the inputs to thesimulator of the present invention (e.g., relative position between thelight source and detector and the central pixel of the detector array).Columns five to column nine indicate the 5 chosen optical parametersdescribing the detected output. In certain embodiments, the follower UUVdetector array samples the incoming light field and the real-timemeasurements are compared to values contained in the aforementioneddatabase. After which, the leader UUV's relative pose is obtained. Theleader UUV's pose parameters y, z, θ and ψ are estimated using thecompiled database. The x-axis coordinate is estimated using thepreviously estimated y, z, θ and ψ.

In certain embodiments of the present invention, the pose detectionalgorithm starts with the determination of the pixel (e,g., detectorarray element) with the greatest light intensity. Then, the poses thatresult in the same maximum pixel intensity location are extracted fromthe database. These poses are referred to as “candidate poses.” Bycomparing the intensity profile of the neighboring pixels with the pixelwith the greatest intensity, any rotational (e.g., pitch and yaw) motioncan be detected. Then, the skewness values (Sk_(x) and Sk_(y)) and SAMangle are subtracted from the candidate pose parameters to obtain a“difference table.” The result is a numerical cost function, P_(i),comprised of the differences of the chosen optical parameters as aweighted sum:

P _(i) =c ₁ |Sk _(x) −Sk _(xi) |+c ₂ |Sk _(y) −SK _(yi) |+c₃|SAM−SAM_(i)|

where, P_(i), Sk_(xi), Sk_(yi) and SAM_(i) represent the penalty,skewness and SAM angle values, respectively, for the candidate pose, i.The parameters c₁, c₂, and c₃ denote the respective weighting factorsfor row and column skewness and SAM angle. Among the chosen candidateposes, the candidate with the lowest penalty score is chosen as the poseestimate.

In certain embodiments, the x-coordinate of the leader vehicle isestimated separately in a two-step procedure. In the first step, a roughestimate of the x-position is obtained based upon the total intensity ofall of the detector array elements. In certain embodiments, acalibration procedure is performed by evaluating the intensities at xcoordinates from 4 m to 8 m at 1 m increments. The sum of theintensities at the detector elements are calculated when the leader andthe follower only have x-offsets between them. The resultant calibrationcurve provides the first x-coordinate estimation as follows:

$x_{{est}\; 1} = 10^{\frac{\log_{10}{(\frac{I_{total}}{12293})}}{- 2.476}}$

In the second step, the x-coordinate estimate from the first step iscorrected by using the estimated relative y, z, θ (pitch) and ψ (yaw)values as follows

x _(est) =x _(est1)−√{square root over (y _(est) ² +z _(est) ²)}″l sin(θ)cos(ψ)

In certain embodiments, the estimated 5-DOF parameters are then used asfeedback to the control system in order to perform the appropriateaction to control the movement of UUVs.

A preliminary analytical study was performed on a leader follower UUVsystem. Both the leader and the follower vehicles were assumed to beidentical with the same mass and inertia and both used the same PIDcontrol parameters (i.e., P=50 and D=8). A generic PID controller wasused, but other controllers know to those of skill in the art can beused. In addition, the leader UUV was given two reference points, R₁ andR₂ while the follower was required to maintain, a relative x-offset of 4m from the leader and to maintain y-axis alignment with the leader UUV(See, for example, FIG. 9). The leader was given step input changes,directed to travel to the specified waypoints. Initially, the leader UUVwas commanded to go from its initial position of (4, 0) to R₁ (4, 0.5).

The control goal for the follower UUV was to follow the leader from 4 mbehind in x-axis direction while maintaining, the same y-axiscoordinate. The trajectories generated by the detection algorithms weresmoothed using a Kalman filter as the distance detection algorithmresulted in a finite resolution, i.e. 0.03 m in y-z axes motiondetection.

As shown in FIG. 10, the performance results of the leader-follower UUVsystem (i.e. detection algorithm and control design) demonstrate thatthe follower UUV maintained the desired fixed distance from the leaderwith acceptable accuracy. Referring to FIG. 10, waypoints R₁ and R₂, theleader (dashed line) and the follower motions (solid line) are shown inthe xy-plane. It is observed, that the leader UUV does not deviate inthe x direction, but has an overshoot in the y-direction at the firstwaypoint. At the second waypoint, i.e. R₂, the leader's PID controllermanages to eliminate the error in the y-direction but results in anovershoot in x-direction.

Contrary to the leader UUV, the follower UUV generates its own desiredtime-varying trajectory by observing and estimating the motion of theleader UUV. The reference trajectory generated by the follower UUV andsmoothed by the Kalman filter resulted in a smoother trajectory than thetrajectories generated by the detection algorithm, especially in y-axis.FIG. 11 and FIG. 12 show the actual leader and follower motions in the xand y-axes, respectively. Overall, the leader UUV completed its taskwith negligible steady-state error in the y-axis and 0.26 m steady-stateerror in the x-axis. The follower UUV managed to keep its distance withthe leader UUV to 3.97 m in the x-axis direction and 0.05 m in they-axis direction. The errors associated with the follower in the twoaxes were 0.03 m and 0.05 m, respectively, and were within the toleranceof the pre-defined control goals.

Referring to FIG. 11, the UUV time-varying x-axis coordinates are shown.The leader UUV's x axis motion (solid line), the follower referencetrajectory generated by the detection algorithm results (dots), and asmoothed trajectory (dashed line) are shown.

Referring to FIG. 12, the leader UUV's y-axis motion are shown. Theleader UUV's x-axis motion (solid line), the follower referencetrajectory generated by the detection algorithm results (dots), and asmoothed trajectory (dashed line) are shown.

In certain embodiments of the system of the present invention, thefollower UUV is able to detect the motion of the leader UUV based onfive parameters (Sk_(x), Sk_(y), the row and column elementscorresponding to a greatest light intensity, and the SAM angle)extracted from the output imagery of the detector array. In certainembodiments, a database is constructed to account for varyingcombinations of relative positions and orientations of the leader UUVwith respect to the follower UUV. Based on a pre-defined course of theleader UUV, virtual real-time distance detection algorithms are appliedusing the intensity measurements from the detector array and thedatabase look up tables.

In certain embodiments, the leader motions are calculated based on rowand column elements in the imagery that are taken as pose candidates. Incertain embodiments, the final pose for the leader position iscalculated based on a calculated cost function that incorporates thedifferences of the skewness of the beam in the imagery andcorresponding; SAM angles.

Preliminary results from simulations that included the leader UUVfollowing two reference waypoints (as step inputs) demonstrate that thecontrol system has good performance. The leader UUV control systemmanaged to maintain the final control goal to within 5% overshoot in thex-axis direction and no overshoot in the yaxis direction. The followerUUV generated its trajectory based on the feedback received from thedetection algorithm and used the Kalman filter to smooth the trajectory.The follower UUV was able to complete its control goal to within anaccuracy of 0.03 m in the x-axis direction and 0.05 m in the y-axisdirection. The follower UUV's motion accuracy was dependent on theaccuracy of its detection algorithm.

Because the follower UUV generates its own time-varying trajectory, itis vital that the reference trajectory is smooth. To compensate for thistime-varying trajectory, a Kalman filter is applied. Although thefollower UUV performed well in maintaining its control goals (e.g.,traveling to a waypoint), better controllers could be implemented forincreased tracking performance. In certain embodiments, a more advanceddetection algorithm is used which is able to provide better motiondetection capability. In certain embodiments, cross-talk during thesimulations, e.g. detection of yaw and pitch motion when the leader'strajectory did not include any rotation, is minimized. In certainembodiments, the implemented control algorithm uses sophisticatedcontrollers specifically designed for nonlinear systems.

In certain embodiments of the present invention, various opticaldetector arrays are designed for the purpose of determining anddistinguishing relative 5 degree-of-freedom (DOF) motion between UUVs:3-DOT translation and 2-DOF rotation (pitch and yaw). In certainembodiments, a numerically based simulator is used to evaluate varyingdetector array designs. In certain embodiments, the simulator includes asingle light source as a guiding beacon for a variety of UUV motiontypes. The output images of the light field intersecting the detectorarray are calculated based on detector hardware characteristics, theoptical properties of water, expected noise sources, and the like. Incertain embodiments, the simulator is used to compare and evaluate theperformance of planar, curved, or other shaped detector arrays (ofvarying sizes). In certain embodiments, output images are validatedusing in situ measurements conducted underwater. Results show that theoptical detector array is able to distinguish relative 5-DOF motion withrespect to the simulator light source. Furthermore, tests confirm thatthe proposed detector array design is able to distinguish positionalchanges of 0.2 m and rotational changes of 10° within 4 m-8 m rangealong the x-axis based on given output images.

Planar and curved array designs for underwater optical detection betweenUUVs or between a UUV and a docking station are compared. The comparisonbetween the two types of arrays is conducted using a simulator thatmodels a single-beam light field pattern for a variety of motion types(i.e., 3-DOF translation and 2-DOF rotation). In addition, the number ofelements in the array and the possible noise sources from experimentalhardware and the environment are also taken into account. The resultsfrom the simulator are validated using in situ measurements conducted inunderwater facilities. These results are used to design an opticaldetector unit for UUVs using translational and rotational detection andcontrol algorithms.

The performance criteria tier an optical detector array design suitablefor underwater communication between UUVs can be judged by twocharacteristics. The first is the ability of the detector array toprovide a unique signature, that is, a sampled image that represents agiven location and orientation of a UUV with respect to a transmitter(e.g., light source). The second characteristic is the minimum number ofrequired optical detector components. A smaller number would simplifythe hardware design and reduce processing time. A unique signature, animage footprint from the optical detectors, enables a UUV to receive thenecessary feedback to help the on-board control system determineappropriate control commands to maintain a specified/desired orientationwith respect to and distance from a beacon (or any other object ofinterest).

The idea behind an optical detector array is such that as this array,which is mounted on a UUV, comes in contact with a guiding beam, or thelike. The light field is sampled and a signature of the light beam isobtained. In certain embodiments, the light source represents a guidethat is mounted on a leader UUV or on a docking station. In certainembodiments, a single light source is used as the guiding beam for thedetector array. The light field generated from the light source isapproximated as a Gaussian beam at a given solid angle. For large arrays(i.e., arrays with several individual detectors), the light signaturecan be further represented as an image.

The design considerations for an optical detector array can becategorized as environmental and hardware-related. In certainembodiments, the primary hardware for such a module consists ofoptoelectronic array components (e.g., photodiodes). These componentsare framed in a specific configuration and are mounted to an appropriatearea on a UUV. A planar array is an array of optical detectors that aremounted on a flat, 2-dimensional frame. Although the optical detectorscan be placed in any configuration, to traditional equidistant design isassumed for the sake of simplicity. The detector, furthermore, isassumed to be square, having an equal number of vertical and horizontalelements (See, for example, FIG. 1B). The planar array simplifies thedesign and the resulting light signature, which is a cross-sectional(and possibly rotated) view of and within the light field.

A curved array is an array of optical detectors that are mounted oneither a spherical or parabolic frame. The geometry of the frame(curvature and oblateness) provides a larger range of incidence anglesbetween the detectors and the light field, in this study, all elementsof the curved array are equidistant in a plane projection and located ata fixed distance from the geometric center of the frame (See, forexample, FIG. 1A).

In certain embodiments, the light source is assumed to be a point sourcewith peak radiance L_(o) (r=0, η=0, Δλ) [W/m²·sr·nm] for a givendetector with a fixed aperture area. Here, r is the distance from thelight source to the optical element, η is the angle between the lightray reaching a detector and the optical axis, and Δλ is the spectralrange as measured by the detector (See, for example, FIG. 1B(2)). Thebeam pattern from the light source is defined as a symmetrictwo-dimensional Gaussian beam pattern:

${L_{0}\left( {0,\eta,{\Delta\lambda}} \right)} = {{L_{0}\left( {0,0,{\Delta\lambda}} \right)} \cdot ^{(\frac{\eta_{2}}{2\sigma^{2}})}}$

where σ is the standard deviation of the light beam.

Referring, to FIG. 1 B(2), the optical detector array and relevantoptical angles are shown. More particularly, the solid line representsthe light ray reaching a detector, the dashed line represents theoptical axis and the dotted line represents the normal to the array. Inaddition to the signal received directly from the light source,background noise, denoted by L_(b), from scattering may occur.Therefore, the effective boundary of the beam area is assumed tocoincide with the area in which the magnitude of the signal is receivedfrom the light source and is equal to that of the background noise.

In addition to the attenuation underwater, the environmental backgroundnoise caused by interaction between the light beam and the water mediumwas modeled. Previous studies investigating the interaction of lightbeams through turbulent medium approximate the background noise using abluffing function applied on the light beam. In certain embodiments, thebackground noise was modeled using a Hanning window:

${h(n)} = {0.5\left( {1 - {\cos \left( \frac{2\pi \; n}{N_{w} - 1} \right)}} \right)}$

where N_(w) denotes the size of the Harming window and n is the samplenumber in the window, i.e. 0≦n≦N_(w)−1. The Hanning window is convolvedwith the output image generated by the optical elements.

As light interacts with a detector element (e.g., photodiode) in thearray, photons from the light are absorbed by the detector and currentis generated. The current is then manipulated by the signal conditioningcircuitry into a digital signal using, an analog-to-digital convertor(ADC). The electrical signal measured by the detector is dependent onthe intensity the optical power) of the light beam and on the detector'sresponsivity (i.e., the electrical output of a detector for a givenoptical input). Also, noise sources produced in the hardware can make itdifficult to extract useful information from the signal. The quality ofthe detector is characterized by the sensitivity which specifies theminimum intensity value that can be detected. In certain embodiments,noise equivalent power (NEP) is used to express the system'ssensitivity. The output current produced from intensity L(r, η, Δλ) iscollected by a detector with a solid angle, Ω, and an entrance aperturearea, A:

i=R·T·L(r, η, Δλ)·A·Ω

where R is the responsivity and T is the throughput of the detector.

In certain embodiments, the key hardware noise sources are: signal shotnoise, σ_(s), background shot noise, σ_(b), dark-current shot noise,σ_(dc), Johnson noise, σ_(j), amplifier noise, σ_(j), and ADC-generatedquantization noise, σ_(q). In certain embodiments, all sources ofhardware noise are assumed to be mutually independent. Furthermore, incertain embodiments, it is assumed that all noise can be approximated asGaussian with corresponding values of standard deviation. Accordingly,these noise sources may be combined as a root sum of squares andrepresented with a net noise current:

σ_(n)=√{square root over (σ_(s) ²+σ_(b) ²+σ_(dc) ²+σ_(j) ²+σ_(q) ²)}

In addition to the electro-optical characteristics of the arraycomponent, the geometrical design of the array also affects the receivedintensity of the light signal. The incidence angle, θ, of the light rayreduces the level of radiance measured by the detector according toLambert's cosine law (See, for example, FIG. 1B(2)):

L _(θ)(r, η, Δλ)=L _(n)(r, η, Δλ)·cos(θ)

where L_(n) is the radiance at the surface normal.

In certain embodiments, the goal of the simulator was to analyze varyingarray designs for UUV optical detection of relative translation androtation with respect to a reference coordinate frame. The criteria inevaluating the effectiveness of a detector array design involved: 1)determining the minimum number of detector elements required for robustUUV position and attitude determination and 2) verifying that thedetector was able to acquire a unique signature for each UUVposition/orientation combination with respect to the given light source.

In certain embodiments, the simulator calculates the light intensitiesat the individual optical elements based on the relative geometrybetween the light source and the detector. The simulator also takes intoaccount the environmental and hardware effects described previously, incertain embodiments, the effective operational distance for underwatercommunication is dependent on water clarity. Although a broad spectralrange of light (400 to 700 nm) can be used for optical communication,the radiation calculation in the simulator can use a narrower spectralrange (e.g., between 500 to 550 nm), providing, maximum transmittance inclear to moderately clear waters.

Based on empirical measurements using, a 400 W metal halide lamp and acommercial grade Mounted Silicon Photodiode photodetector (NEP Rangebetween 1×10⁻¹⁴ to 5×10⁻¹⁴ W·Hz^(−1/2)), a maximum operational distanceof up to 20 m was assumed for extremely clear waters, which representedopen ocean conditions (K=0.05 m⁻¹), and of up to 8 m for moderatelyclear waters, which represented tropical coastal waters (K=0.1 m⁻¹).Although the simulator provided results for larger angles, pitch androll angles were limited to within 20°. This constraint was based on theassumption that most UUVs are built to be stable about their pitch androll axes of rotation.

In certain embodiments, in the simulator of the present invention, anEarth-fixed reference frame is assumed, where as light source iscentered at the origin (0,0,0). Several coordinates are identified inthe x-y-z coordinate frame with respect to the UUV center of mass (COM).Several attitude orientations are also identified with respect to theEarth-fixed reference frame and defined by angles φ, θ, and Ψ for roll,pitch, and yaw, respectively. In order to ensure appropriate sensorfeedback for adequate control performance, the detector array should beable to detect a unique light, signal (pattern) for each combination ofcoordinate position and attitude orientation. In certain embodiments,this detection should be accurate to within 0.2 m of the true COMcoordinate position and to within 10° of the true attitude orientationwithin 4 m-8 m range along the x-axis.

In certain embodiments, the array geometry is chosen based upon thedimensions of the UUV. The UUV in this study was assumed to be a rigidbody of box-type shape with a width (starboard to port) and height (topto bottom) of 0.4 m and a length (from bow to stern) of 0.8 m, which isthe size of a generic observation-class ROV used as a test platform. Itis understood that various shapes and dimensions could be used dependingon the desired application. In certain embodiments, the adaptedcoordinate axes convention is that of the Tait-Bryan angles, where thex-axis points toward the bow and the y-axis towards starboard, and thebody-fixed z-axis points downward and completes the orthogonal triad.

As previously mentioned, two array shapes were compared in Applicants'studies: (1) a planar array and (2) a curved array. It is understoodthat a variety of shapes could be used. The geometry of the planar andcurved arrays is defined below.

In the planar detector array, the detectors are defined relative to theUUV COM with respect to the local (body) coordinate flame. The centerand the four corners of the planar array frame are defined as follows:

${Arr}_{center} = \left( {{{COM}_{x} + \frac{1}{2}},{COM}_{y},{COM}_{Z}} \right)$${Arr}_{{\min {(y)}},{\max {(y)}}} = {{COM}_{y} \pm \frac{w}{2}}$${Arr}_{{\min {(z)}},{\max {(z)}}} = {{COM}_{z} \pm \frac{h}{2}}$

where COM_(x), COM_(y), and COM_(z) respectively define the x, y, and zcoordinates of the follower COM, l is the length of the UUV, and w and hdenote the width and the height of the vehicle, respectively. Thelateral and vertical spacing (denoted as p_(y) and p_(z), respectively)between the individual detectors on the array can be expressed as:

$p_{y} = \frac{w}{N - 1}$ $p_{z} = \frac{h}{N - 1}$

It is assumed that the detector array is an N×N square where N is thenumber of optical elements. That is, the number of detectors in the rowsand columns of the array are the same. Accordingly, the detectorspacing, is also the same (i.e. p_(y)=p_(z)).

A hemispherical shape is used for the curved array. The number ofdetectors in the curved, array is initially defined based on the N×Nplanar array design. Then, if the detectors are projected onto thehemisphere surface, as in FIG. 1A, with a fixed radius r:

x _(ij)=√{square root over (r ² −y _(ij) ² −z _(ij) ²)}

where x_(ij) is the position of the detector element on the x-axis andy_(ij) and z_(ij) are the coordinates of the array that is projectedonto the bow of the follower UUV. In addition, i and j are the indicesthat represent the row and column number of the array, respectively. Theradius, r, of the hemisphere is defined from its focal point, F, whichis the center of the hemisphere.

$F_{x} = {{COM}_{x} + \frac{1}{2}}$ F_(y) = COM_(y) F_(z) = COM_(z)

In certain embodiments, the hemispherical radius of the curved array iskept longer than the width or height of the planar array in order tohave the same number of elements for both array designs. In certainembodiments, the main difference between the two array designs is thatall of the optical elements in the planar array are oriented in the samedirection, while the detectors in the curved array are normal to thesurface of the array frame and thus allow a larger range of incidenceangles.

The construction of a realistic light signal (as measured by the arraydetectors) is based on the radiometric and hardware considerations foreach detector. The radiometric calculations are based on the distance(using the inverse square law and Beer's law) and orientation (usingLamberts cosine law) of each detector with respect to the light source.Using the detector's characteristics and the associated electronics, theartificially created incident light was numerically converted into adigital signal. In certain embodiments, the specifications of two typesof photodiodes were used as references (Hamamatsu SM05PD1A and HamamatsuSM05PD2A). The resulting electronic signal was represented as a 10-bit(0-1023) sensor output value (thus, introducing quantization error). Incertain embodiments, environmental background noise is artificiallyadded to the signal using a Hanning window of size N_(w)=11. Also, arandom net noise current of σ_(n)=10⁻⁶ can be added to the electronicsignal. In certain embodiments, the final digital signal is used togenerate an image pattern, which, in turn, is to be used by the arraydetectors to identify the position and the orientation, of the UUV.

Although the UUV is a six DOF system, it is assumed that it is notpossible to achieve relative roll angle detection (because of axialsymmetry about the body x-axis). In certain embodiments, only fiveparameters are provided to the simulator as input: translation along,all three coordinate axes, rotation of the pitch angle, θ, and rotationof the yaw angle, ψ. Accordingly, the image output of the simulator isanalyzed using five parameters that can be related to input parameters(See, for example, FIG. 13): the peak light intensity value, l, thecorresponding location of the horizontal detector, j, and verticaldetector, k, at peak intensity, the location, of the skewness of thehorizontal intensity profile gradient, Sk_(h), and skewness of thevertical intensity profile gradient, Sk_(v). The peak value isnormalized with respect to a given maximum detectable intensity(0.0<I<1.0). The locations of the horizontal and vertical detectors aredefined with respect to the central detector (j=(N+1)/2, k=(N+1)/2).

Based on the location of the peak intensity, the slopes of thehorizontal and vertical intensity are calculated. In certainembodiments. The slope of the profile is used rather than the profileitself because the slope also provides the directionality of the beamprofile (i.e., negative or positive) in addition to the asymmetry of theprofile. The images and the corresponding parameters for the planar andthe curved array of size 21×21 for a given coordinate location and yawrotation are shown in FIG. 13 and FIG. 14, respectively.

Referring to FIG. 13, key image parameters and intensity profiles for aplanar array detector unit with hardware and environmental backgroundnoise are shown: (top left) Output image from the simulator, (top right)Horizontal profile, (bottom left) Vertical profile, (bottom right) Inputvalues used to generate output image and key parameters describing, theoutput image.

Referring to FIG. 14, key image parameters and intensity profiles for acurved array detector unit with hardware and environmental backgroundnoise are shown: (top left) Output image from the simulator, (top right)Horizontal profile, (bottom left) Vertical profile, (bottom right) Inputvalues used to generate output image and key parameters describingoutput image.

As a first step for the selection of the array design, the geometry ofthe detector array was evaluated. A performance evaluation betweenplanar and curved arrays was conducted, where each detector arraycontained, a 21×21 grid of detector elements. Both detector arrays wereevaluated for their ability to detect changes in position andorientation, i.e., changes in SAM angle. In certain embodiments, changesin position are evaluated as the UUV translates along the y-axis from agiven origin (0 m) to an offset of 0.9 m in 0.03 m increments.Similarly, changes in orientation are evaluated by rotating the UUVabout the z-axis, yaw rotation, from its initial reference (0°) to 30°in increments of 1°. Resemblance results that were used to identify UUVpositional and attitude changes based on measured signals (images)collected by the detector array at 4 m are presented in FIG. 15. Thecomparative results for changes in position using the SAM algorithm showsimilar performance between the two array geometries, where the curvedarray performs slightly better (2°) at shifts greater than 0.6 m.However, an investigation of the results for changes in orientationreveals that the curved array is more sensitive to changes inorientation than the planar array. The SAM angle results for the curvedarray shows changes of 12° at 5° yaw rotations and changes of 22° at 10°rotations, whereas the planar array shows changes in SAM angle of 5° at5° yaw rotations and 11° at 10° rotations. Based on these results, it isdeduced that the curved array geometry may be more suitable fordistinguishing changes in position and especially, orientation of a UUVplatform with respect to a reference light beacon.

In certain embodiments, alter the geometry of the detector array isdefined, relationships between the ability to distinguish changes inposition and orientation from the output images and the number ofelements in the curved detector array are evaluated. The comparisonsincluded different array sizes, ranging from a 3×3 size array up to a101×101 size array at distances ranging from 4 m to 8 in to the lightsource. The comparative results at 4 m (FIG. 16) show that changes inpositional and rotational shifts can be detected by an array with thesize of at least 5×5 optical elements. Based on a threshold of a 15° SAMangle, a smaller array would fail to detect translational shifts smallerthan 0.2 m or rotational changes smaller than 10°. It should also benoted that no significant changes in detection capability were observedfor array sizes greater than 7×7. The effect of operational distancesgreater than 4 m is shown in FIG. 17. Although the ability of the curvedarray to distinguish between the images decreases as the operationaldistance increases, the SAM algorithm results for 5×5 array at 8 m arestill above 10° for a 10° yaw rotation and above 6° for 0.2 mtranslation.

In certain embodiments, the simulator of the present invention has amodular design to allow for the addition and changing of hardware andenvironmental parameters. In certain embodiments, the simulator canevaluate other array geometries with a variety of sizes, in addition tothe two traditional shapes considered herein. The simulator results showthat a curved array with a minimum array size of 5×5 elements issufficient for distinguishing positional changes of 0.2 m and rotationalchanges of 10°. For the distinction of smaller changes, a larger arraysize may be useful.

In certain embodiments, a follower UUV is assumed to have five DOFmaneuverability with respect to a given light source: three DOFtranslation (i.e., translations along the x, y, and z axes) and two DOFrotation (yaw and pitch). In certain embodiments, the transmitter unithas only one light source with a Gaussian spatial intensitydistribution. This can complicate the decoupling of roll changes(rotation about the body-fixed x-axis) from either pitch or yaw. This isdue to the axial symmetry of the light beam. In certain embodiments, theuse of multiple light sources or a light source with a unique intensitydistribution can enable roil rotation sensing.

It is important to note that the simulator assumes that the water columnis uniform with systematic background noise. As a result, the outputimages of the light field intersecting with the detector array have aresemblance with a Gaussian beam pattern. However, disturbances in themedium (e.g., sediment plume) may cause the beam pattern to bedistorted. This point should be taken into account in the development ofcontrol algorithms for UUV navigation. Otherwise, the control algorithmsmay misinterpret the acquired image and direct the follower UUV awayfrom the guiding beam. The simulator results show that detector noisedoes not contribute significantly to the image output. Other detectorswith a larger noise level may contribute more to output images.

Referring to FIG. 18, arrays for certain embodiments of the presentinvention are shown. Referring to FIGS. 19-22, various detected imagesat 4 m for certain embodiments of the present invention are shown. Moreparticularly, referring to FIG. 19, the top two images represent a101×101 array, and the two bottom images represent a 51×51 array. Stillreferring to FIG. 19, the images on the left are from planar arrays andthe images on the right are from curved arrays. The bottom images inFIG. 19 also include noise. Referring to FIG. 20, 5×5 arrays are shown,where the left image is from a planar array with noise and the image onthe right is from a curved array with noise. Referring to FIG. 21, a11×11 array is shown. Referring to FIG. 22, a 21×21 planar array isshown.

While the principles of the invention have been described herein, it isto be understood by those skilled in the art that this description ismade only by way of example and not as a limitation as to the scope ofthe invention. Other embodiments are contemplated within the scope ofthe present invention in addition to the exemplary embodiments shown anddescribed herein. Modifications and substitutions by one of ordinaryskill in the art are considered to be within the scope of the presentinvention.

What is claimed:
 1. An optical communication instrumentation system forleader-follower formations of unmanned underwater vehicles comprising, aleader unmanned underwater vehicle and a follower unmanned underwatervehicle, a light source mounted on the leader unmanned underwatervehicle producing a 3-dimensional light field, an optical detector arraymounted on the follower unmanned underwater vehicle for detecting thelight field an algorithm for controlling and detecting distance andcontrolling motion and orientation between the leader unmannedunderwater vehicles and the follower unmanned underwater vehicle.